@book{Tu_DiffGeo,
    AUTHOR = {Tu, Loring W.},
     TITLE = {Differential geometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {275},
      NOTE = {Connections, curvature, and characteristic classes},
 PUBLISHER = {Springer, Cham},
      YEAR = {2017},
     PAGES = {xvi+346},
      ISBN = {978-3-319-55082-4; 978-3-319-55084-8},
   MRCLASS = {53-01},
  MRNUMBER = {3585539},
       DOI = {10.1007/978-3-319-55084-8},
       URL = {https://doi.org/10.1007/978-3-319-55084-8},
}
@book{WangLiu_DiffGeo,
    AUTHOR = {王幼宁 and 刘继志},
   ADDRESS = {北京},
     TITLE = {微分几何讲义},
 PUBLISHER = {北京师范大学出版社},
      YEAR = {2017},
  LANGUAGE = {chinese}

}
@book{doCarmo_RiemGeo,
    AUTHOR = {do Carmo, Manfredo Perdig\~{a}o},
     TITLE = {Riemannian geometry},
    SERIES = {Mathematics: Theory \& Applications},
 PUBLISHER = {Birkh\"{a}user Boston, Inc., Boston, MA},
      YEAR = {1992},
     PAGES = {xiv+300},
      ISBN = {0-8176-3490-8},
   MRCLASS = {53-01},
  MRNUMBER = {1138207},
MRREVIEWER = {Bang-yen Chen},
       DOI = {10.1007/978-1-4757-2201-7},
       URL = {https://doi.org/10.1007/978-1-4757-2201-7},
}
@book{Euclid_Elem,
  author         = {欧几里得},
  editor         = {兰纪正 and 朱恩宽},
  editortype     = {译},
  publisher      = {陕西科学技术出版社},
  address        = {西安},
  title          = {几何原本},
  year           = {2003},
  language       = {chinese}
}
@article{Klein_Erlangen,
    AUTHOR = {Klein, Felix},
     TITLE = {Vergleichende {B}etrachtungen \"{u}ber neuere geometrische\\
              For\-schun\-gen},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {43},
      YEAR = {1893},
    NUMBER = {1},
     PAGES = {63--100},
      ISSN = {0025-5831},
   MRCLASS = {DML},
  MRNUMBER = {1510801},
       DOI = {10.1007/BF01446615},
       URL = {https://doi.org/10.1007/BF01446615}
}
@book{Zorich_MathAnal,
    AUTHOR = {Zorich, Vladimir A.},
     TITLE = {Mathematical analysis. {I}},
    SERIES = {Universitext},
   EDITION = {Second},

 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2015},
     PAGES = {xx+616},
      ISBN = {978-3-662-48790-7; 978-3-662-48792-1},
   MRCLASS = {00A05 (00-01 26-01)},
  MRNUMBER = {3495809},
       DOI = {10.1007/978-3-662-48792-1},
       URL = {https://doi.org/10.1007/978-3-662-48792-1},
}
@book{Mei_Manifold,
  author         = {梅加强},
  publisher      = {科学出版社},
  title          = {流形与几何初步},
  address        = {北京},
  year           = {2013},
  language       = {chinese}
}
@book{Tu_IntroMani,
    AUTHOR = {Tu, Loring W.},
     TITLE = {An introduction to manifolds},
    SERIES = {Universitext},
   EDITION = {Second},
 PUBLISHER = {Springer, New York},
      YEAR = {2011},
     PAGES = {xviii+411},
      ISBN = {978-1-4419-7399-3},
   MRCLASS = {58-01 (53-01 57-01)},
  MRNUMBER = {2723362},
       DOI = {10.1007/978-1-4419-7400-6},
       URL = {https://doi.org/10.1007/978-1-4419-7400-6},
}
@book{Lee_IntroTopoMani,
    AUTHOR = {Lee, John M.},
     TITLE = {Introduction to topological manifolds},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {202},
   EDITION = {Second},
 PUBLISHER = {Springer, New York},
      YEAR = {2011},
     PAGES = {xviii+433},
      ISBN = {978-1-4419-7939-1},
   MRCLASS = {57-01 (54-01 55-01)},
  MRNUMBER = {2766102},
       DOI = {10.1007/978-1-4419-7940-7},
       URL = {https://doi.org/10.1007/978-1-4419-7940-7},
}
@book{Lee_IntroSmMani,
    AUTHOR = {Lee, John M.},
     TITLE = {Introduction to smooth manifolds},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {218},
   EDITION = {Second},
 PUBLISHER = {Springer, New York},
      YEAR = {2013},
     PAGES = {xvi+708},
      ISBN = {978-1-4419-9981-8},
   MRCLASS = {58-01 (53-01 57-01)},
  MRNUMBER = {2954043},
       DOI = {10.1007/978-1-4419-9982-5},
       URL = {https://doi.org/10.1007/978-1-4419-9982-5}
}
@book{Lee_ManiDiff,
    AUTHOR = {Lee, Jeffrey M.},
     TITLE = {Manifolds and differential geometry},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {107},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2009},
     PAGES = {xiv+671},
      ISBN = {978-0-8218-4815-9},
   MRCLASS = {53-01 (58-01)},
  MRNUMBER = {2572292},
MRREVIEWER = {Richard H. Escobales, Jr.},
       DOI = {10.1090/gsm/107},
       URL = {https://doi.org/10.1090/gsm/107},
}
@book{Rotman_AdvMdnAlg,
    AUTHOR = {Rotman, Joseph J.},
     TITLE = {Advanced modern algebra. {P}art 1},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {165},
   EDITION = {Third},
 PUBLISHER = {American Ma\-thematical Society, Providence, RI},
      YEAR = {2015},
     PAGES = {xiv+706},
      ISBN = {978-1-4704-1554-9},
   MRCLASS = {00-01 (12-01 13-01 14-01 16-01 18-01 20-01)},
  MRNUMBER = {3443588},
MRREVIEWER = {Srikanth B. Iyengar},
       DOI = {10.1090/gsm/165},
       URL = {https://doi.org/10.1090/gsm/165},
}
@book{Spivak_CalMani,
    AUTHOR = {Spivak, Michael},
     TITLE = {Calculus on manifolds. {A} modern approach to classical
              theorems of advanced calculus},
 PUBLISHER = {W. A. Benjamin, Inc., New York-Amster\-dam},
      YEAR = {1965},
     PAGES = {xii+144},
   MRCLASS = {26.20 (57.00)},
  MRNUMBER = {0209411},
MRREVIEWER = {C. B. Allendoerfer},
}
@article{McGrath_HBT,
    AUTHOR = {McGrath, Peter},
     TITLE = {An extremely short proof of the hairy ball theorem},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {American Mathematical Monthly},
    VOLUME = {123},
      YEAR = {2016},
    NUMBER = {5},
     PAGES = {502--503},
      ISSN = {0002-9890},
   MRCLASS = {55M25},
  MRNUMBER = {3508974},
       DOI = {10.4169/amer.math.monthly.123.5.502},
       URL = {https://doi.org/10.4169/amer.math.monthly.123.5.502},
}
@article{Tarski_Axiom,
     title = {Tarski's System of Geometry},
    volume = {5},
       DOI = {10.2307/421089},
    number = {2},
   journal = {Bulletin of Symbolic Logic},
 publisher = {Cambridge University Press},
    author = {Tarski, Alfred and Givant, Steven},
      year = {1999},
     pages = {175–214}
}
@book{doCarmo_DiffForm,
    AUTHOR = {do Carmo, Manfredo P.},
     TITLE = {Differential forms and applications},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1994},
     PAGES = {x+118},
      ISBN = {3-540-57618-5},
   MRCLASS = {58A10 (53-01 53A05 58-01)},
  MRNUMBER = {1301070},
MRREVIEWER = {Frans Cantrijn},
       DOI = {10.1007/978-3-642-57951-6},
       URL = {https://doi.org/10.1007/978-3-642-57951-6},
}
